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Brief notes on Sixsigma
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Lean Six Sigma Training
Define
Measure
Analyze
Examples
six sigma project people selection.
Define: Why is there such a difference is the sales performance of people?Measure: Top people have 10X volume of the bottom 25%. Failure to meet sales quotas is a defect.Analyze: Education, training, time in job, product line, sales area, profiles.Improve: Able to identify by profile 72% of the top sales people. Use this tool to select new people into this function.Control: Use profiles for new hires and continue to monitor performance levels.
six sigma project new capacity justified.Define: Contract to deliver product at a minimum rate on a daily basis. Severe penalties if rate missed by even a small
amount. Customer "good will" also an issue.Measure: Capacity of units in the system more than the minimum rates. Collected failure rate data for each unit and time to repair.Analyze: Failure rate data combined with the time to repair data indicated that there were significant periods of time when the minimum contract rates could not be met and penalties would be paid.Improve: Capital approved for an additional unit. Within the first year the new unit was required at least four separate times for several weeks each time to meet the contract minimums. Any one of the four times returned enough cash to pay for all of the capital expended.Control: System to tract and monitor failure data and repair time data.
six sigma project web design. Define: Design a web site that ranks in the top ten (10) on all major search engines and directories.
Measure: Enter "six sigma" and check ranking in search engines.Analyze: URL name, title of pages, and other factors are major ranking criteria. Reciprocal links and other routine activities aid in search engine ranking.Improve: Purchase URL with six sigma included, optimize each page, develop reciprocal links, and perform other regular activities required to maintain traffic and ranking.Control: Monitor ranking on search engines weekly. You can check on the success of this project by entering "six sigma" in the search field of your favorite search engine. Success is a link to http://www.adamssixsigma.com in the top ten (10) listings. The titles and descriptions may vary , the URL link is the performance measure
DefinitionsTerm Definition
Customer Focus The concept that the customer is the only person qualified to specify what Quality means.
Process ExcellenceA set of techniques for ensuring that key processes are identified, owned, strategically aligned, and continuously monitored and improved
DMC DMC is Define-Measure-Control methodology for implementing Process Excellence
DMAICData Driven strategy to Improve Processes, A quality initiative as part Six Sigma methodology ( Define , Measure , Analyze, Improve, Control)
LEAN Lean is a way to continuously eliminate waste
Kaizen Change for better through Continuous Improvement by Involvement of All
WasteWaste is anything that takes time , resources , or space but does not add to the value of the product or service delivered to the customer
6 Types of Waste Defect , Motion , In- efficiency , Waiting , Over- Processing and Inventory
SIPOC SIPOC (suppliers, inputs, process, output, and customers) is a tool to define a process.
CTQ "Critical to Quality" requirements of a customer from a product or service
Kano Analysis Kano analysis is a technique used to prioritize customer requirements.
ProcessA Process Is A Collection Of Activities That Takes One Or More Inputs and creates output that is of Value to the Customer
Continuous DataData that can be measured on a continuum / scale ; and can be meaningfully subdivided into finer & finer increments.
Discrete Data Data that is categorized into distinct buckets ; values can't be subdivided further meaningfully.
Performance Standard Customer expectation of performance on the CTQ's.
Defect Any event of failure to meet the performance standard
LSL Lower Specification Limit : the minimum value the customer is willing to tolerate on a metric.
USL Upper Specification Limit : the maximum value the customer is willing to tolerate on a metric.
Defective Any unit having one (or more) defects
DefinitionsTerm Definition
Cycle time Total time required to complete a process step(s)
TAT Total elapsed time ( Time Taken to Complete a Transaction or Activity)
Yield Yield is the percentage of a process output that is free of defects.
Unit A unit is any item/entity that is produced or processed.
Opportunity Opportunities are the measurable and distinct ways in which a defect can be created.
DPMO Defects per Million Opportunities
DPO Defects per Opportunity
DPU Defects per Unit
Sigma levelThe Greek letter (sigma) refers to the standard deviation of a population. Sigma level is a measure of Process capability.
Process Capability Process capability refers to the ability of a process to produce a defect-free product or service.
Sampling Sampling is the practice of gathering a subset of the total data available from a process or a population.
Dashboard Tool used for Collecting & Reporting Information - Good dashboards are visual & graphic.
Histogram A graphic representation of variation in a set of continuous data.
Standard Deviation A statistic used to measure the variation in a distribution
Mean The mean is the average data point value within a data set.
MedianThe median is the middle point of a data set; 50% of the values are below this point, and 50% are above this point.
Normal DistributionThe charting of a data set in which most of the data points are concentrated around the average (mean), thus forming a bell shaped curve
Scatter plot A scatter plot is a basic graphic tool that illustrates the relationship between two variables.
DefinitionsTerm Definition
ScorecardA scorecard is an evaluation device, your customers will use to rate your business's performance in satisfying their requirements.
BenchmarkingBenchmarking is a continuous process whereby an enterprise measures and compares all its functions, systems and practices against strong competitors, identifying quality gaps in the organization, and striving to achieve competitive advantage locally and g
Entitlement As good as a process can get without Re-design
Variation Variation is the fluctuation in process output.
Fish Bone DiagramA Cause and Effect Analysis Technique. A diagram which explores the relationship between the problem and its causes (by category).
Transfer function Transfer Function Y= f(X), describes the relationship between outputs (Y) & input / process(x) metrics.
FMEA Failure Modes & Effect Analysis
Mistake Proofing A technique for "Eliminating Errors" and "Making it Impossible" to make mistakes
Poka -yoke Japanese term which means mistake proofing, To avoid (yokeru) inadvertent errors (poka).
ProbabilityProbability refers to the chance of something happening, or the fraction of occurrences over a large number of trials.
Probability of Defect Probability of defect is the statistical chance that a product or process will not meet performance specifications
Robust Process A robust process is one where quality of output is immune to variation in inputs.
Control limitsAlso called "Voice of Process" : reflect the expected variation in the process , based on the distribution of the data points.
BQCBusiness Quality Council- is Steering Committee to review and guide on Quality Initiatives aligned with Business needs
BBFull Time Six Sigma Trained resource who completes High Impacts Projects to Improve Process Performance, reduce defects and enhance Customer Satisfaction. BB also mentors Green Belts
MBBMaster Black Belts are Six Sigma Quality experts that are responsible for the strategic implementation within an organization. Master Black Belt's main responsibilities include training and mentoring of Black Belts and Green Belts.
GBSix Sigma Trained resources with a full time functional / operational responsibility - who do DMAIC projects to Improve Process Performance.
YB Yellow Belt- Trained in DMC methodology, implement Process Excellence
D-M-A-I-C…Overview
Step 1: Identify VoC & CTQs
Step 2: Define the Project
Step 3: Define Process map
Step 4: Building Team & Commitment
Step 5: Assess Risk
Step 1: Identify and prioritize CTQ Metrics
Step 2: Define Performance Standards
Step 3: Measurement System Analysis & Data Collection Plan
Step 4: Establish Current Process Capability
Step 5: Quantify the Opportunity
Step 1: Brainstorm potential solutions
Step 2: Screen solutions against criteria
Step 3: Develop Implementation Plan
Step 1: Develop Control Plan
Step 2: Develop Process Management Flowchart
Step 3: Assess Potential Problems
Step 4: Implement Process Control System
Step 1: Identify Root Cause / Sources of Variation
Step 2: Validate Root Causes
Step 3: Define Performance Objectives
Step Description
Define
Measure
Analyze
Improve
Control
D-M-A-I-C…Define Objectives
Step 1: Identify VoC & CTQs
Step 2: Define the Project
Step 3: Define Process map
Step 4: Building Team & Commitment
Step 5: Assess Risk
Step Description
DefineSelecting the Project
8
Define-Beginning With An Idea
Customer wants andneeds should drive
our actions!
Who’s the customer? What does he/she think is critical
to quality? Who speaks for the customer?
What’s the business strategy? Who in the business holds a stake
in this? Who can help define the issues? What are the processes involved?
Sources Of Project Ideas
Customer dashboards
Surveys
Scorecards
BQC
Kaizen
FMEA
Using Scorecard to Identify Projects
CTQs for Ramp Process Excluded
Additional YB Trg Conducted instead of LSS Awareness Program
Defects – 210, Volume - 89610
Defects – 3192, Volume - 112761
Selecting Right Project
L M HUnderstanding of how to solve problem
“Boiling the Ocean”
“Just Do It”
“Looking Good”
“Why Bother?”
H
M
L
Quick Wins
Six Sigma Projects
Bu
sin
ess
or
Cu
sto
mer
Imp
act
Impact - Critical to Customer , Critical to BusinessKnowledge - Solution UnknownSpeed - Results in 3-6 monthsProject meets ROI expectations (e.g. savings level)
Project has available resources (BB, GB)
Project has clear sponsorship and process ownership
A defect or opportunity can be measured
Selecting The Right Projects
Issues in selecting a project:
Feasibility (Is it doable?)
Measurable impact
Potential for improvement
Resource support within the organization
Project Selection
Success Factors
– Project scope is manageable
– Project has identifiable defect
– Project has identifiable impact
– Adequate buy-in from key stakeholders To be Successful…
– Set up project charter and have it reviewed
– Measure where defects occur in the process
– Assess and quantify potential impact up front
– Perform stakeholder analysis Common Pitfalls
– Resourcing of project is inadequate
– Duplicating another project
– Losing project momentum
– Picking the easy Y, not the critical Y Avoiding Pitfalls…
– Identify and get committed resources up front
– Research database and translate where possible
– Set up milestones and communications plan
Optimize on the Success Factors to Maximize Six Sigma Project Benefits.
Optimize on the Success Factors to Maximize Six Sigma Project Benefits.
Project Activity (20 minutes)
Answer the following questions as they relate to your project:
1. What are you improving?
2. When are you finishing?
3. What is the impact?
4. Potential for Improvement:
5. What is the difference between needed and available resources?
6. How many similar project are running across Processes
.
Define – Identify VoC & CTQs
Step 1: Identify VoC & CTQs
–Voice of the Customer
–Product/Process Drill-Down Tree
–Take Always-Identify Project CTQ’s
Step 2: Define the Project
Step 3: Define Process map
Step 4: Build Team & Commitment
Step 5: Assess Risk
Define
What is critical to the quality of the process?…according to your customer!
What is critical to the quality of the process?…according to your customer!
Who Is The Customer?
Customer–Whoever receives the output of your process
– Internal Customer vs. External Customer
Output–The material or data that results from the operation of a process
Process–The activities you must perform to satisfy your customer’s
requirements
Input–The material or data that a process does something to or with
Supplier–Whoever provides the input to your process
CustomerProcessInput Output
Supplier
Voice Of The Customer (VOC)
Definition: What is critical to the quality of the process according to your customer.
Key VOC tools:
Surveys
Focus Groups
Customer Complaints Customer Communication
Research MethodAdvantages/Disadvantages
Advantages: Lower cost approach Phone response rate 70-90% Mail surveys require least amount of
trained resources for execution Can produce faster results
Disadvantages: Mail surveys can get incomplete results,
skipped questions, unclear understanding Mail surveys 20-30% response rate Phone surveys: interviewer has influential
role, can lead interviewee, producing undesirable results
Advantages: Group interaction generates
information More in-depth responses Excellent for getting CTQ definitions Can cover more complex questions
or qualitative data
Disadvantages: Learnings only apply to those asked,
difficult to generalize Data collected typically qualitative vs.
quantitative Can generate too much anecdotal
information
Focus GroupsFocus Groups
SurveysSurveys
Research MethodAdvantages/Disadvantages
Advantages: Specific feedback Provides opportunity to respond
appropriately to dissatisfied customer
Disadvantages: Probably not adequate sample size May lead to changing process
inappropriately based on 1-2 data points
Advantages: Can tackle complex questions
and a wide range of information Allows use of visual aids Good choice when people won’t
respond willingly and/or accurately by phone/mail
Disadvantages: Long cycle time to complete Requires trained, experienced
interviewers
Customer ComplaintsCustomer Complaints
InterviewsInterviews
Project Activity (10 minutes)
For your project:
What tool did you can use for capturing VOC?
List all customers and the segment(s) from which
you can captured VOC
Process/Product Drill–Down Tree
Six Sigma Projects work on removing defectson selected CTQ’s by improving processes.
Six Sigma Projects work on removing defectson selected CTQ’s by improving processes.
• Customer requirements (customer CTQ’s)
• Process requirements (process CTQ’s)
How Customer CTQ’s Become Project CTQ’s
Important To Our Customer
Sub-Process/Service
B
Sub-Process/Service
C
Product/Process/Service
Single Cell Projects
Process-Based Projects
CT
Q P
roje
cts
Con
trol
labl
e B
y U
s
Define product and/or process treeand identify product and process
CTQ’s
Define product and/or process treeand identify product and process
CTQ’s
Sub-Process/Service
A
Process 4
Process 1
Process 2
Process 3
CTQ9CTQ1 CTQ2 CTQ3CTQ4 CTQ5 CTQ6 CTQ7 CTQ8
Example: CTQ Drill–Down Tree
Knowledgeable Accessible Accurate Fast
Closing Receive $
Timely
Process
Loan ApplicationReliable, Quick
CanAnswer
Questionscorrectly
ExceptionalCustomerService
Level 1 CTQ
Level 2 CTQ
Rec’s‘right’Loan
24 hrAccess
Access From Anywhere
ClearLoanApp
SimpleLoan App
72 hrResponse
Requestsfor more
Info within24 hrs
Level 3 CTQ
Select Loan
Complete
App
Underwrite
Exercise: Process/Product Tree
Your task:
Based on all previous Define work,
draw a CTQ Drill-Down tree for
your project
Take Aways–Identify Project CTQ’s
A successful project is focused on the customer and is clearly bound
with defined goals
To determine project CTQ’s the customer and their wants must be
determined. Critical to Quality characteristics (CTQ’s) are determined
by the customer
A successful project is related to one or more of the four Vital
Customer CTQ’s:
– Customer Responsiveness/Communication
– Market Place Competitiveness-Product/Price/Value
– On-Time, Accurate, and Complete Customer Deliverables
– Product/Service Technical Performance
Project CTQ’s are integrated with the business strategy through the
process/product drill-down tree
Define – Identify VoC & CTQs
Step 1: Identify VoC & CTQs
Step 2: Define the Project–Team Charter
–Business Case
–Problem & Goal Statements
–Project Scope
–Milestones
–Team Roles
–Good Project vs. Bad Project
–Take Aways-Develop Team Charter
Step 3: Define Process map
Step 4: Managing Change & Build Commitment
Step 5: Assess Risk
Define
Team Chartering
A Charter:– Clarifies what is expected of the team– Keeps the team focused– Keeps the team aligned with organizational priorities– Transfers the project from the champion to the
improvement team
27
Five Major Elements Of A Charter
Business Case– Explanation of why to do the project
Problem and Goal Statements– Description of the problem/opportunity and objective
in clear, concise, measurable terms
Project Scope– Process dimensions, available resources
Milestones– Key steps and dates to achieve goal
Roles– People, expectations, responsibilities
The Business Case
Why is the project worth doing?
Why is it important to do it now?
What are the consequences of NOT doing the
project?
What activities have higher or equal priority?
How does it fit with the business initiatives and
target?
Problem And Goal Statements
The purpose of the Problem Statement is to describe what is wrong
The Goal Statement then defines the team’s
improvement objective
Problem & Goal Statements Together provide focus and purpose for the team.
Problem Statement
The Problem Statement is an objective description of the “pain” experienced by internal and/or external customers as a result of a poorly performing process.
– What is wrong or not meeting our customer’s needs?
– When and where do the problems
occur?– How big is the problem?– What is the impact of the problem?
The Problem Statement
Key Considerations/Potential Pitfalls– Is the problem based on observation (fact) or
assumption (guess)?– Does the problem statement prejudge a root cause?– Can data be collected by the team to verify and
analyze the problem?– Is the problem statement too narrowly or broadly
defined?– Is a solution included or implied in the statement?– Would customers be happy if they knew we were
working on this?
The Goal Statement
Project Objective– Definition of the improvement the team is seeking to
accomplish?– Starts with a verb (reduce, eliminate, control,
increase)– Tends to start broadly–eventually should include a
measurable target and completion date– Must not assign blame, presume cause, or prescribe a
solution!
SMART Problem And Goal Statements
A methodology for evaluation is called “SMART.”
This acronym is a checklist to ensure that the charter
is effective and thorough.
SMART
Specific Does it address a real business problem?
Measurable Are we able to measure the problem, establish a baseline, and set targets for improvement?
Attainable Is the goal achievable? Is the project completion date realistic?
Relevant Does it relate to a business objective?
Time Bound Have we set a date for completion?
Project Scope
What process will the team focus on?
What are the boundaries of the process we are to improve?
Start point? Stop point?
What resources are available to the team?
What (if anything) is out-of-bounds for the team?
Under what (if any) constraints must the team work?
What is the time commitment expected of team members?
What are the advantages to each team member for the time
commitment?
Steps To Bound A Project
Identify the customer
– Who receives the process output?
–(May be an internal or external customer) Define customer’s expectations and needs
– Ask the customer
– Think like the customer
– Rank or prioritize the expectations Clearly specify your deliverables tied to those expectations
– What are the process outputs? (Tangible and intangible deliverables)
– Rank or prioritize the deliverables
– Rank your confidence in meeting each deliverable Identify CTQ’s for those deliverables
– What are the specific, measurable attributes that are most critical in the deliverables?
– Select those attributes that have the greatest impact on customer satisfaction
Steps To Bound A Project (continued)
Map your process
– Map the process as it works today (as is)– Map the informal processes, even if there is no formal, uniform
process in use Determine where in the process the CTQ’s can be most seriously affected
– Use a detailed flowchart– Estimate which steps contain the most variability
Evaluate which CTQ’s have the greatest opportunity for improvement
– Consider available resources– Compare variation in the processes with the various CTQ’s– Emphasize process steps which are under the control of the
team conducting the project Define the project to improve the CTQ’s you have selected
– Define the defect to be attacked
Team Roles
How do you want the Sponsor to work with the team?
Is the team’s role to implement or recommend?
When must the team go to the Sponsor for approval? What
authority does the team have to act independently?
What and how do you want to inform the Sponsor about the team’s
progress?
What is the role of the team leader (Black/Green Belt) and the team
coach (Master Black Belt)?
Are the right members on the team? Functionally? Hierarchically?
Team Charter–Breakout Activity
How Who Time
TeamPreparation
Choose a facilitator, timekeeper, scribe, and/or note taker.
All 1 min.
Write problemand goalstatement
For your own project, write a problem and goal statement using the guidelines in this section .
Individuals or partners
15 min.
Critique Exchange problem and goal statements with others in your group and provide suggestions for improvement.
All 15 min.
Brainstorm key challenges in preparing a good charter.
Choose a spokesperson to report your identified challenges to the group.
Facilitator
All
Work
Close Exercise 5 min.
A Good Project
A good project:– Problem and goal statement is clearly stated– Defect and opportunity definition is clearly understood– Does not presuppose a solution– Clearly relates to the customer and customer’s requirements– Aligns to the business strategy– Uses the tools effectively – Is data driven
A bad project: – Is not focused-scope is too broad– Is not clear on what you are trying to fix– Is not an already known solution mandated without proper investigation– Is difficult to see linkage to customer needs– Is not clearly aligned with business objectives– Has little or no use of tools– Is anecdotal-not data driven
Define – Process Map
Step 1: Identify VoC & CTQs
Step 2: Define the Project
Step 3: Define Process map– High Level Process Map (SIPOC)
– Detail Process Map
Step 4: Managing Change & Build Commitment
Step 5: Assess Risk
Define
What Is A Process?
A process is any related, recurring sequence of events, steps, activities, or tasks which result in a desired outcome.
Processes must have steps that repeat each time the process is used.
Processes can be defined as either core or enabling.–Core processes: things that we “must do.”
–Enabling processes: series of tasks and activities that are internal to the business but contribute to the performance of core processes.
Process Mapping
Objectives
– Learn the definition of process mapping
– Understand business processing mapping and its Application to completely satisfying customer requirements
– Learn the key process elements
– Learn the importance of process boundaries and process owners
– Understand the benefits of process mapping
– Understand the steps of process mapping
Process Mapping Definition
Process Mapping Is the Graphic Display of Steps, Events
and Operations That Constitute a Process
A tool used to:– Clearly define processes
– Identify areas where data collection should take place
– Visualize activities involved in a process at the early stages of project development
– Establish the process boundaries
– Observe the process in operation
– List the outputs, customers, and their key requirements
– List the inputs, suppliers, and your key requirements
Benefits Of Process Mapping
Can reveal unnecessary, complex, and redundant
steps in a process. This makes it possible to simplify
and troubleshoot.
Can compare actual processes against the ideal. You
can see what went wrong where.
Can identify steps where additional data can be
collected
Perceptions Of A Process
What we think it looks like:
What it actually looks like:
What we wish it would look like:
Do not jump to “What we wish it would look like”.Do not jump to “What we wish it would look like”.
Building A Map
Determine the scope
– How complex and detailed a map do you need to give
you what you want?
Determine the steps in the process
– Don’t worry about order
– Don’t worry about priorities
– Just list them!
Arrange the steps in order
Assign a symbol (see next page)
To Identify Areas Of Improvement, Processes Must Be Decomposed Into Sub Processes
MarketSegmentation
Design Offer Promotion
Marketing Advertising Sales
ObtainCustomer
DeliverProduct/Service
AccountingCustomer
ServiceCore Process
Sub-process
Sub-process
Two Decomposition And Analysis Techniques Are In This Section: 1) Top-down Charting; 2) Functional Deployment Process Maps
To gain significant insight into how work is actually completed, one must understand processes.
Process mapping is a technique used to document and analyze processes.
Process mapping identifies the flow of a process that any service or product follows.
The two most commonly used process mapping tools are the top-down chart and the functional deployment process map.
Top-Down Charts: document a core process and its related sub-processes.
Functional Deployment Process Maps: document sub-processes, the sequence of individual steps and decisions, and who is responsible for them.
Top-down Charting Uses Two Levels Of Detail: Process And Sub-process
Top-Down Charting
Process ________________________________________________________
Sub-processes
__________ __________ __________ __________ __________
Start Stop
Define your hard start and stop to the process before
doing the steps.
Functional Deployment Mapping Is Used To Further Define And Understand A Sub-process Activity
Core Process
Steps
ResponsibleClerk Supervisor Materials
ManagementScheduler
Log-in Order
Prioritize Order
Review for Specifications
Materials Explosion
Schedule Fabrication
Inspection
Distribution
N
N
Y
Y
Top-Down Charting Functional Deployment Mapping
Start & End Points
Identify the boundaries of the process.
Activity What is being done. Indicates necessary and unnecessary activities performed in the process.
Decision Illustrates decision points and where loops occur in the process. Also used to accept, reject, approve, etc.
Arrow Represents a process path/flow.
Input or Output Shows important inputs or outputs without describing in detail.
Process Connectors
Connect flow to another page or process.
A# Activity Number Shows the activity in the sequence performed.
D# Decision Number Shows the decision points in the sequence performed.
Standard Symbols Are An Integral Component To Completing A Functional Deployment Process Map
NOTE: Yes-arrows stem from the bottom of the diamond, symbolizing the quickest way to customer satisfaction.
No
Yes
Using Proper Symbols, A Descriptive And Accurate Functional Deployment Map Can Be Created
Sub-processes
Entry Order
Approve Credit
Procurement
Manufacturing
Request
Routing
Shipping
Billing
Department
Sa
les
Off
ice
Ord
er
De
pt
Cre
dit/
Co
llect
.
Inve
n.
Co
nt.
Tra
ffic
Sh
pg
/ R
ec
Mig
. /
QC
Pu
rch
asi
ng
Bill
ing
Acc
ts /
Re
c
A1
A4 A3 A2
A5 A6 A7 A8
A9 D1
D2
A10A11
A12
A13 A14 A15 A16 A17 A18
D3 A19 A20 A21 A22
There Are A Few Helpful Hints To Keep In Mind When Creating A Deployment Process Map
Define your hard start and stop to the process before doing the steps.
Keep it simple. Use as few words as possible to label columns and describe work
steps.
If work flows into and out of the process: Create a separate column and label it
“outside,” or create columns where the headings reflect where the flow goes
(department head, engineering, etc.).
Include the individuals involved in a process on the process mapping team. These
are the employees who are most familiar with a process and who will have to live
with any future process changes.
A common view of the process rarely exists at the outset. Individual team
members who possess a detailed knowledge about a unique part of the process
do not always consider how each part relates to the big picture.
Exercise
Case Study Exercise
Process Mapping
Exercise: Project Process Mapping
ObjectiveTo practice developing process maps
Instructions–As a project team, use either the Top Down Method or the
Functional Deployment Map method and draft a process map for “Origin to end of Life of Transaction”
Exercise
Define – Building Team & Commitment
Step 1: Identify VoC & CTQs
Step 2: Define the Project
Step 3: Define Process map
Step 4: Building Team & Commitment – Team Building
– Align Roles & Processes
– Building Commitment from Stakeholders
Step 5: Assess Risk
Define
Steps towards Success
SCOPE -
GOALS -
ROLES -
TimingOrganizations InvolvedProcesses InvolvedLevels Involved
Results / Target for ProjectMeasurements of Success
Who Should be on Project Team?What is Their Role?
Project Definition
Boundaries:
Who outside our team must we involve, inform or consult with?
What decisions need approval from someone outside our team?
What is not in our scope of work (though others might think it is)?
What authority does the team have to act independently?
Roles and Responsibilities:
What is the reporting relationship to the Team Sponsor?
What role and area(s) of responsibility does each team member
have?
What unique responsibilities does the Team Leader have?
Operating Agreements:
How will the team make decisions; resolve conflicts?
What are acceptable/unacceptable levels of involvement?
How often and how long will we meet as a team?
Steps towards Success
59
Building Team
Key Stakeholders
PROJECT PHASE
Startup/Planning Implementation Evaluation
What: A tool to determine individuals and/or groups whose commitment is essential for project success
Why: To ensure that the project leader has identified Key Stakeholders
How: List individuals/groups involved in the process and identify project function
When: Team Building
What Role People play in our Project ?
Key Stakeholders
PROJECT PHASE
Startup/Planning Implementation Evaluation
A Approval of team decisions outside their charter authorities, e.g., sponsor, business leader
R Resource to the team, one whose expertise, skills, or clout may be needed on an ad hoc basis
M Member of team, with the authorities and boundaries of the charterI Interested party, one who will need to be kept informed on direction and
findings, if later support is to be forthcoming
A-R-M-I …an example
DEFINE MEASURE ANALYZE IMPROVE CONTROL
Sponsor A,I A,I A,I A,I A,I
MBB A A A A A
BB R, I R, I R, I R, I R, I
GB (Leader) M M M M M
Member R R,M R,M R,M R,M
Member M M M M M
Member M M M M M
KEY STAKE HOLDERS Function
Goals-Roles-Processes-Interpersonal Check List
An excellent organizing tool for newly-formed teams or for teams that have been underway for a while, but who have never taken time to look at their teamwork. Ideally, this tool should be used at one of the first team meetings. It can and should be updated as the project unfolds.
GOALS–How clear and in agreement are we on the mission and goals of our team/projects?
Low High
1 2 3 4 5
ROLES–How well do we understand, agree on, and fulfill the roles and responsibilities for our team?
PROCESSES–To what degree do we understand and agree on the way we’ll approach our project AND our team? (Procedures and approaches for getting our project work done? For running our team?)
INTERPERSONAL–Are the relationships on our team working well so far? How is our level of openness, trust, and acceptance?
Goals Roles Process Interpersonal Check list
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
How would you rate the degree to which your team presently has CLARITY, AGREEMENT, and EFFECTIVENESS on the following related elements?
0% 25% 50% 100%
Purposes & OutcomesWe understand and agree on our project mission and the We understand and agree on our project mission and the desired outcome (vision).desired outcome (vision).
Customer & Needs We know who the project stakeholders are, what they We know who the project stakeholders are, what they require, and why this project is really require, and why this project is really needed.needed. Goals & Deliverables We have identified specific, measurable and prioritized We have identified specific, measurable and prioritized project goals and deliverables linked project goals and deliverables linked to our business goals.to our business goals. Authority & Autonomy (Scope) We understand/agree on what’s in/out of our project scope We understand/agree on what’s in/out of our project scope and tasks. The project scope is “set”.and tasks. The project scope is “set”.
GOALS
R&R
Roles & ResponsibilitiesWe have defined and agreed on our roles, responsibilities, We have defined and agreed on our roles, responsibilities, required skills, and resources for our required skills, and resources for our
project team.project team. Authority & Autonomy Our team is clear on the degree of authority/empowerment Our team is clear on the degree of authority/empowerment we have to meet our project mission.we have to meet our project mission.
Goals-Roles-Processes-Interpersonal Check List
0% 25% 50% 100%
PROCESS
INTERPERSONAL
Critical Success FactorsWe know and are focusing on the key factors needed to We know and are focusing on the key factors needed to meet the project goals and mission.meet the project goals and mission.
Plans & Activities We have an effective game plan to follow that includes the We have an effective game plan to follow that includes the right tasks, clearly right tasks, clearly defined/assigned.defined/assigned. Monitoring & Measures We have an effective monitoring process and specific We have an effective monitoring process and specific metrics linked to progress and metrics linked to progress and goals.goals. Schedule/Milestones We have defined our project schedule and know what the We have defined our project schedule and know what the
key phases and milestone are.key phases and milestone are.
Team Operating AgreementWe have shared expectations, agreed and followed We have shared expectations, agreed and followed guidelines for how our team works guidelines for how our team works
together.together. Interpersonal/Team We have the necessary relationships, trust, openness, We have the necessary relationships, trust, openness, participation and behaviors for a participation and behaviors for a healthy and productive healthy and productive team. team.
Goals-Roles-Processes-Interpersonal Check List
Stakeholder Analysis
Steps:
1. Plot where individuals currently are with regard to desired change ( = current).
2. Plot where individuals need to be (X = desired) in order to successfully accomplish desired change–identify gaps between current and desired.
3. Indicate how individuals are linked to each other; draw lines to indicate an influence link using an arrow ( ) to indicate who influences whom.
4. Plan action steps for closing gaps.
NamesStronglyAgainst
ModeratelyAgainst
Neutral ModeratelySupportive
StronglySupportive
StakeholderName/Title
or ConstituentStronglyAgainst
ModeratelyAgainst Neutral
ModeratelySupportive
StronglySupportive
Reasons for Rating
Stakeholder Analysis Contd…
Names SA MA N MS SS Issues / Concerns “Success Indicators Influence Strategy
Stakeholder Analysis / Influence Strategy
Stakeholder S.H Issues/Concerns
Influence StrategyIdentify S.H.“Wins”
Desired New Behaviors What Who By When
Influence Strategy
Media(written, events,
one-on-one, etc.)
Message(inform, persuade,
empower)
Target Audience
Who When / Where
Communication Planning Worksheet
objective
Work Planning In Team
Action/TaskWho When
Breakout Activity (25 minutes)
Desired Outcomes
To practice identifying Stakeholders and their support relative to your project
What How Who TimeTeamPreparation
Choose a facilitator, scribe, timekeeper,and/or note taker
Determine timing for each activity belowCreatepreliminaryStakeholderAnalysis
Individuals
Closeexercise
All
Using the Stakeholder Analysis worksheet provided:
– List key stakeholders for your project.– Identify their current level of support.– Determine where you need them to be in
order for the project to be successful.
Choose a spokesperson to report out on top 2-3 key elements of your influence strategies
All 5 min.
20 min.
Define – Assessing Risk
Step 1: Identify VoC & CTQs
Step 2: Define the Project
Step 3: Define Process map
Step 4: Building Team & Commitment
Step 5: Assess Risk
– For the Project
– From the Project on
Define
Assess the Risk for ProjectAssess the Risk
• For the Project
• on Process/Customer due to Project
For the Project
•What is probability of Failures of My Project
•What will Fail
•How it will fail
•What action are required to prevent
•Who are responsible for these actions
•Timelines to complete these actions
Use FMEA methodology to assess Risk for the Project
•on Process/Customer due to Project
•What are the process / Customer CTQs gets affected
•What is the probability of negative impact
•Identify all risks
D-M-A-I-C…Overview
Step 1: Identify VoC & CTQs
Step 2: Define the Project
Step 3: Define Process map
Step 4: Building Team & Commitment
Step 5: Assess Risk
Step 1: Identify and prioritize CTQ Metrics
Step 2: Define Performance Standards
Step 3: Measurement System Analysis & Data Collection Plan
Step 4: Establish Current Process Capability
Step 5: Quantify the Opportunity
Step 1: Brainstorm potential solutions
Step 2: Screen solutions against criteria
Step 3: Develop Implementation Plan
Step 1: Develop Control Plan
Step 2: Develop Process Management Flowchart
Step 3: Assess Potential Problems
Step 4: Implement Process Control System
Step 1: Identify Root Cause / Sources of Variation
Step 2: Validate Root Causes
Step 3: Define Performance Objectives
Define
Measure
Analyze
Improve
Control
Content Flow
• Transfer Function
• Y & X
• Difference between Xs and Segmentation
• Using Statistics to Solve real problem
• Statistics software – Minitab
• Using data for Understanding variation
• Continuous Vs discrete Data
• Sources of Variation
• Type of variation
• Describing Variation over a period of Time
• Statistics
• Distribution
•Shape
•Normal curve
•Normal Probability
• Histogram
•Statistics
• Central Tendency
• Descriptive Statitics
• Variation
• Histogram
• Measures of Variation
• Variation over a Period of Time…Display
• Run Chart
• Two Types Of Variation
• Analyzing Relationships
• Scatter diagram
• Pareto
Content Flow
• Establish Process Capability
• Identify your Project Y data Type
For Continuous Data
• Identify the Data- Normal & Non Normal
• Check Stability- Run Chart
• Check Distribution & Spread
• Calculate Process Capability- Sigma Value, DPMO – Capability Analysis
For Discrete data
• Calculate Process Capability- Sigma Value, DPMO – Capability Analysis
• First Pass Yield
• Cumulative Yield Calculation
Content Flow
• Identify Sources of Variation
• Brainstorm for Possible sources of Variation – Fishbone Diagram, 5-Why
• Prioritize all Possible Xs – Control/Impact Matrix
• Validate Prioritized Xs
• Validation of Process as X
• Type of Work – Waste
• Nature of Work – VA/NVA/VE
• Flow of Work – Sub Process Map
• Data Analysis
• Hypothesis Testing
• List of Validated Xs
Content Flow
• Define Performance Objective
• Benchmarking
• Other sources
Content Flow
80
Terminology
Project YDependent
Independent X(5M’s and 1P)
Independent Variables–X’s Also called factors Factors or variables we select in advance The causes
Dependent Variable–Y Also called responses The quantity (Y) that we measure to determine
the impact of the X’s The effect
Project Y
MMM
M MP
(x) (x) (x)
(x) (x) (x)
81
Bridging The Real World
Practical SolutionPractical Solution
Statistical SolutionStatistical Solution
Practical ProblemPractical Problem
Statistical ProblemStatistical Problem
ProblemSolving
Flow State current process sigma.
Identify distribution’s characteristic causing current process sigma: shape,
center and/or spread.
Find X’s that lead to better process sigma: Identify the levels of X’s
Identify process change that incorporates statistical solution
© 1994 Dr. Mikel J. Harry V3.0
82
The Nature Of Statistical Problems
© 1994 Dr. Mikel J. Harry V3.0
Problem with Spread
DesiredCurrent
Situation
LSLLSL USLUSLTT
Accurate but not PreciseAccurate but not Precise
Problem with Centering
Desired
LSLLSL USLUSLTT
Precise but not AccuratePrecise but not Accurate
CurrentSituationOff Target
83
Using Statistics To Solve Problems
Y = ƒ (X1, …, Xn)
Goal: To find the relationship
P(x)
x
Data-Driven AnalysisData-Driven Analysis
84
Using Statistics To Characterize Processes
Likelihood
Likelihood
Minitab and Graphical Analysis Module ObjectivesUnderstand the structure of Minitab*
Understand data entry and correct data structure for analysis in Minitab
Review variation
Be able to create and interpret basic graphs in Minitab
Minitab Windows
Graph WindowGraph Window
Menu BarMenu Bar
Session Window:• Analytical Output
Session Window:• Analytical Output
Data Window:• A Worksheet, not a
Spreadsheet
Data Window:• A Worksheet, not a
Spreadsheet
Data Window
Minimizes the Window Closes the Window
Maximizesthe Window
Scroll Bars
Data Entry Arrow
Column NamesAre Entered Here
Data is EnteredHere
Minitab Menus–Summary
File Menu
Edit Menu
Data Menu
Calc Menu
Stat Menu
Graph Menu
Print and save the window that is currently active File menu changes depending on the window that is currently active Allows open, close, and save
Similar to the edit menu in most standard Windows applications
Sort, code or manipulate data
Calculate or generate data
Basic statistics and quality tools Most often used by Green Belts
Contains the commands that you will use to do graphical analysis during your project
Help Menu Minitab has a comprehensive Help system with detailed documentation of all features, complete with examples of how all the menu commands are used, and how to interpret graphical and statistical output which result from the use of the commands
Window Menu Allows you to manage multiple graphs on the screen
Using Minitab: A Typical Session1. Enter data
2. Select menu command (for desired statistical/graphical function)
3. Enter command parameters in the dialog window
4. View results in session window or graph window
5. Copy output to another application
6. Print output
7. Save file
Using Minitab: A Typical SessionStep 1: Enter Data Minitab allows you to enter data in four different ways:
1. Open an existing Minitab worksheet
2. Type data into the worksheet
3. Import data files from other compatible software packages
4. Paste data from other applications
Using Minitab: A Typical SessionStep 1: Enter Data
Type data directly into worksheet
Using Minitab: A Typical SessionStep 1: Enter Data
1.3 How to import an Excel data file:
1. File > Open Worksheet
2. Select Files of Type: Excel
3. Highlight the file to be imported
4. Double-click or click Open
Using Minitab: A Typical Session
Step 1: Enter DataPaste data from Excel
1.In Excel:Highlight Data (and Column Names) to be copiedUsing Your Mouse
2.Copy the Data to the Windows ClipboardEdit > Copy (or CTRL-C on Your Keyboard)
3.Go to Minitab:ALT > Tab
4. Position the Cursor where you want the data to fillSee example below.
5. Go to the Edit Menu:Edit > Paste/Insert Cells (or Ctrl-V on the keyboard)
Insertion point
Using Minitab: A Typical SessionStep 1: Enter Data
Tips for moving data back and forth:Structure the data so that each variable is in a single column
Each column must have a title
The column title must have fewer than 31 characters and be on a single line
All data must immediately follow the column names
Do not put empty rows between rows of data
Columns containing dollar signs or commas cannot be transferred to Minitab using Copy or Paste, but can be imported using the import command. Reformat these numbers to include only decimal points.
After movement into Minitab, check column heading type (D vs. T.)
Using Minitab: A Typical SessionStep 1: Enter Data.
Tables vs. Variable Columns
The best format for analysis of data in Minitab is variable columns.
Sales Office January February March AprilCentral 387,980 45,700 456,789 349,050Southwest 578,990 600,987 456,789 456,798Northeast 435,800 542,700 345,988 564,050Southeast 497,050 827,900 456,789 687,050Northwest 613,242 61,689 456,789 434,567
Sales Office Revenue MonthCentral 387,980 JanuaryCentral 45,700 FebruaryCentral 456,789 MarchCentral 349,050 AprilSouthwest 578,990 JanuarySouthwest 600,987 FebruarySouthwest 456,789 MarchSouthwest 456,798 AprilNortheast 435,800 JanuaryNortheast 542,700 FebruaryNortheast 345,988 MarchNortheast 564,050 AprilSoutheast 497,050 JanuarySoutheast 827,900 FebruarySoutheast 456,789 MarchSoutheast 687,050 AprilNorthwest 613,242 JanuaryNorthwest 61,689 FebruaryNorthwest 456,789 MarchNorthwest 434,567 April
Graphical Analysis Of DataKey Questions:
How is my data distributed (variation)?
What relationships exist between the Y variable and X variables?
Review–VariationAll repetitive activities have variation (fluctuation)
Variation is a primary source of customer dissatisfaction
In order for our customers to “feel the quality” , we must reduce variation
Using Data To Understand Variation Plot The Data Using Variation Tools
Mea
sure
men
t
Time
Fre
quen
cy
Measurement
Histogram Run Chart
Study Variation For A Period Of Time Study Variation Over Time
– Histogram
Box Plot
Bar Chart
Pie Chart
Histogram
Run Chart
Control Chart
Control Charts
Run Chart
For Continuous Data For Discrete Data For Continuous Data For Discrete Data
Review–Continuous vs. Discrete DataReminder: Data Type Is Critical!
Data type dictates how much variation we will see:Continuous data–the most information about variation in the process
Discrete data–less information about variation in the process
Application Cycle TimeUpper Specification Limit = 30 Days
DiscreteY = late/on-time
No. Rec’d No. Late
30 2
Less variation information
ContinuousY = days to process
USL
The most variation information
28 23 13 34 24 29 21 16 24 11 49 21 21 25 26 27 27 29 30 29 30 20 10 30 12 11 27 23 24 28 17 9 30 29 29 28
Actual Times
5 M’s & 1 PSources Of Variation
Machines
Methods
Materials
Measurements
Mother Nature
People
PROCESS
PROCESS
Two Types Of VariationCommon Versus Special Causes
To distinguish between common and special causes variation, use display tools that study variation over time such as Run Charts and Control Charts.
Common Cause
Special Cause
Type of Variation Characteristics
Always Present Expected
PredictableNormal
Not Always Present Unexpected
UnpredictableNot Normal
Characteristics
Describing Variation For A Period Of Time: Data Distributions
Key Questions:What is the shape of the distribution–symmetrical, lopsided, cliff-like shape, twin peaks, flat?
What is the central tendency (“center ” or “average”) of the distribution?
What is the variation (“spread”) of the distribution–wide or narrow?
StatisticsStatistics is concerned with making inferences about general populations and about characteristics of general
populations
We study outcomes of random experiments
If a particular outcome is not known in advance, then we do not know the exact value assigned to the variable of that outcome:
The number of invoices received weekly
The cost in dollars of reworking each part
The number of surfaces that are rough on a cast part
The number of calls received every Monday between the hours of 8-9 a.m.
We call such a value a random variable
Some DistributionsA random variable can be expressed in terms of a distribution
Uniform Distribution
Single roll of dice
All permissible values p(x) are equally likely
Triangular Distribution
Sums of pairs of dice
Rapidly descending P(X), no tails
P(X)
X
P(X)
X
DistributionsNormal Distribution
Process/repair times
Error fluctuations about an operating point
Exponential Distribution
Time between arrivals
Time between random (unrelated) failures
Events with no memory from one to the next
P(X)
X
P(X)
X
ShapeShape is the distribution pattern exhibited by the data
Assess shape using a histogram, or more precisely with a Normal Probability Plot
12 13 14 15 16 17 18 19
0
1
2
3
4
5
6
7
Fre
qu
en
cy
Roughly Normal Distribution
7 9 11 13 15 17 19 21 23
0
1
2
3
4
5
6
Fre
qu
en
cy
Bimodal Distribution0 10 20 30 40 50 60 70 80 90
0
10
20
Skewed Distribution
Fre
qu
en
cy
The Normal Curve
Is The Data Distribution Normal?
Definition:A probability distribution is where the most frequently occurring value is in the middle and other probabilities tail off symmetrically in
both directions.
Characteristics:The curve does not reach zeroThe curve can be divided in half with equal pieces falling either side of the most frequently occurring valueThe peak of the curve represents the center of the processThe area under the curve represents 100% of the product the process is capable of producing
The Normal Curve (continued)
Specific Characteristics
68.26% Fall Within +\- 1 Standard Deviation
95.46% Fall Within +\- 2 Standard Deviation
99.73% Fall Within +\- 3 Standard Deviation
-3s -2s -1s X +1s +2s +3s
68.26%
95.46%
99.73%
34.13% 34.13%
13.60% 13.60%2.14% 2.14%
0.13% 0.13%
Normal Probability PlotAlternate Description Of Shape
Average: 16.3921StDev: 5.61675N: 240
Anderson-Darling Normality TestA-Squared: 0.208P-Value: 0.864
2 12 22 32
.001
.01
.05
.20
.50
.80
.95
.99
.999
Pro
babi
lity
Cycle Time
Normal Probability Plot
Normal Probability Plot (continued)
Straight line Skewed Long-TailedBimodal curve
12 13 14 15 16 17 18 19
0
1
2
3
4
5
6
7
Fre
quen
cy
Roughly Normal Distribution
Per
cent
Normal Probability Plot for a Normal Distribution
ML Estimates
Mean:
StDev:
0 10 20 30 40 50 60 70 80 90
0
10
20
Skewed Distribution
Fre
quen
cyP
erce
nt
Normal Probability Plot for a Skewed Distribution
ML Estimates
Mean:
StDev:
15.0790
12.6232
Per
cent
Normal Probability Plot for Long-Tailed Distribution
0 10 20 30
1
5
10
20
3040506070
80
90
95
99
7 9 11 13 15 17 19 21 23
0
1
2
3
4
5
6F
requ
ency
Bimodal Distribution
0 10 20 30
1
5
10
20
3040506070
80
90
95
99
Per
cent
Normal Probability Plot for aBimodal Distribution
ML Estimates
Mean:
StDev:
14.6382
5.47084
7 9 11 13 15 17 19 21 23
0
1
2
3
4
5
6
Fre
quen
cy
Long-Tailed Distribution
Distribution Type:
Straight line Two lines(Stable Operations)
“S” curveZig-zag
How Distribution Looks On Normality Curve:
If you conclude that Y is non-normally distributed, there are two general approaches:
Approach : Variance-based Thinking (VBT) Methodology
possibly multiple processes embedded
segmentation and stratification
Range reduction
What If Your Data Is Not Normal?
Expectation: Green Belts Should Be Able To DO Approach 1
“Center” Or Central Tendency
Descriptive Statistics:
Represents the nominal value of the process.
Mean ( )
Median (“middle” data point)
Quartile Values (Q1, Q3) x
Q1 Q3
Normal Distribution
Long-tailed Distribution
Skewed Distributions
X
“Center” Or Central Tendency (continued)The Mean, sometimes called the average, is the most likely or expected value. The formula for the mean is:
The Median is literally the middle of the data set where 50% of the data is greater than the median, and 50% of the data is less than the median. The most commonly used symbol for the median is . The procedure for calculating the median is:
Order the numbers from smallest to largest If the number of values (N) is odd, the median is the middle value. For example, if the ordered values are 3, 4, 6, 9, 20, the median is 6.If the number of values (N) is even, the median is the average of the two middle values. For example, if the ordered values are 1,5,8,9,12,18, the median is
8.5.For very skewed data, we can describe the central tendency in terms of the quartile values, Q1 or Q3.Q1 is the data point that divides the lowest 25% of the data set from the remaining 75% and is used to describe performance when the data is
skewed toward the right.Q3 is the data point that divides the highest 25% of the data set from the remaining 75% and is used to describe performance when the data is
skewed toward the left.
1. The sum of all data values
2. Divide by number of data valuesn
XX i
X~
VariationDescriptive Statistics
Represents the variation ofthe process
Standard Deviation (s)
Range
Q1
s
Q1Q3 Q3
Normal Distribution
Long-tailed Distribution
Skewed Distributions
x=.05 x=.95
Variation For A Period Of TimeDescriptive Statistics Summary
Shape Normality Plot Center Spread(central tendency) (variation)
normal
skewed
long-tailed
Quartile Q1 or Q3
Standard Deviation (s)
Stability Factor (SF)
Span
bimodal
Normal Probability Plot for a Normal Distribution
Per
cent
ML EstimatesMean:
StDev:
15.7224
1.74183
Normal Probability Plot for an Exponential Distribution
Per
cent
ML EstimatesMean:StDev:
15.079012.6232
Normal Probability Plot for a Long-Tailed Distribution
Normal Probability Plot for a Bimodal Distribution
0 10 20 30
1
510
20304050607080
9095
99
Per
cent
ML EstimatesMean:StDev:
14.63825.47084
0 10 20 30
1
510203040506070809095
99
Per
cent
ML EstimatesMean:StDev:
14.63825.47084
The different processes must be stratified before descriptive statistics
can be calculated.
Mean X
Median X~
Displaying Variation For A Period Of TimeHistogram
Illustrates
Central tendency (center) of the data Variation (spread) of the data
Shape (pattern) of the data
Measurements
10 11 12 13 14 15 16 17 18 19
0
5
10
Time Estimates (in seconds)
# of
Occ
urre
nces
Histogram of Time Estimates
Graphical DisplayTime
EstimatesRound 1
16.4818.8913.1811.1114.6716.5314.7918.0614.4814.8915.6313.9513.7417.6710.2313.6711.3515.03
13.8413.5015.4114.3514.3714.6313.5814.7511.9514.3616.1715.1512.4814.1219.0013.8112.9714.19
TimeEstimatesRound 2
Displaying Variation For A Period Of Time (continued)
Box Plots
Highest Value
Third Quartile (75%) value
Lowest Value
First Quartile (25%) value
Median
*
Each segment represents 25% of the data points
Outlier
Summary–Variation For A Period Of Time
10 11 12 13 14 15 16 17 18 19
0
5
10
28 23 13 34 24 29 21 16 24 11 49 21 21 25 26 27 27 29 30 29 30 20 10 30 12 11 27 23 24 28 17 9 30 29 29 28
Data
Histogram
Variation Over TimeRun Chart
A graphical tool to monitor the “stability of Project Y
Allows observation of time order properties such as trend
Should be used before any detailed data analysis
Example of a Run Chart
Median
Is the process stable over time?
Run Charts–Special Cause PatternsIf p < 0.05, then there is significant statistical evidence to show that one of the trends below exists.
Cluster
Oscillating Trend
Mixture
Two Types Of VariationInvestigating Common vs. Special Causes
For new process data, use a Run Chart to look for special causesInvestigate special cause points for positive quick-fixes
Common cause variation requires systematic improvement effort
Two Types Of Variation (continued)
Reacting To Common vs. Special Causes
How you interpret variation . . .
Common Causes Special Causes
Common
Causes
Special
Causes
Mistake 1Tampering
(increases variation)
Focus on systematicprocess change
Mistake 2
Under-reacting(missed prevention)
Investigatespecial causes for possible quick-fixes
Truevariation
type...
Graphical Analysis Tools
Continuous Y Discrete YBoxplot
Pareto ChartScatterplot
Looking For Patterns In Data
Box PlotsWhat differences do you see between the output from the different shifts?
Shift 6Shift 5
Shift 4Shift 3Shift 2
Shift 1
60
30
10
Mea
sure
Scatter Diagrams–Analyzing RelationshipsUse Scatter Diagrams To Study The Relationship Between Two Variables.
Cyc
le T
ime
(D
ays)
(Y
)
Size Of Loan (X)
40
30
25
20
15
10
5
35
1K 2K 3K 4K 5K 6K 7K 8K 9K 10K
Warning! Correlation Does Not Imply CausationCorrelation Between Number Of Storks And Human Population
Number Of Storks
50100
80
70
60
200 30050
80
70
60
100 200 300
Source: Box, Hunter, Hunter. Statistics For Experimenters. New York, NY: John Wiley & Sons. 1978
Population (In Thousands)
Interpretation Of A Scatter DiagramLook For:
Common patterns in the data
Range of the predictor variable (X)
Irregularities in the data pattern
Interpreting A Scatter DiagramLook For Patterns
No Correlation
Positive Correlation
Strong Positive Correlation
Other PatternNegative Correlation
Strong Negative Correlation
11
22
33
44
55
66
For all charts: Y = Participant satisfaction (scale: 1 – worst to 100 – best)X = Trainer experience (# of hours)
Common Scatter Diagram Patterns
Potential Cause
Eff
ect
Potential Cause
Eff
ect
Plot +/- OtherStrong,
Weak, Other Example
1
2
3
Potential Cause
Eff
ect
Common Scatter Diagram Patterns (continued)
Potential Cause
Eff
ect
4
Potential Cause
Eff
ect
5
Potential Cause
Eff
ect
6
Plot +/- OtherStrong, Weak,
Other Example
Common Scatter Diagram Patterns (continued)
Potential Cause
Eff
ect
7
Potential Cause
Eff
ect
8
Potential Cause
Eff
ect
9
Plot +/- OtherStrong,
Weak, Other Example
Common Scatter Diagram Patterns (continued)
Potential Cause
Eff
ect
10
Potential Cause
Eff
ect
11
Potential Cause
Eff
ect
12
Plot +/- OtherStrong,
Weak, Other Example
Pareto ChartsIs There A Defect That Occurs Frequently?
C A E D B
Frequency
Category of Defect
Establish Process Capability
In this step your team:– Calculates baseline process capability for the process
Why is this step important?
This phase is important because it clearly defines how well the process is currently performing and identifies how much the process will be improved.
What is establishing Process capability
What does it mean to Establish Process Capability?
Process capability refers to the ability of a process to produce a defect-free product or service. In this step, you will determine how consistently your product or process meets the performance standard for your project Y calculating the sigma level. The sigma level is calculated through statistical analysis of the collected data.
Why is it important to Establish Process Capability?You can’t set a measurable goal without a clear understanding of where you are. It is important to establish process capability in order to baseline your current process performance. This will be the starting point from which you will set your improvement goals.
What are the project tasks for completing Step 4?4.1 Graphically analyze data for project Y (continuous data only)4.2 Calculate baseline sigma for project Y
Step 4.1: Graphically Analyze Data ForProject Y
Review: Describing Variation
Prior to Calculating Capability, we need to know:
Key question #1–Stability–Variation over time (Run Chart)
How stable is the data?
Key Question #2–Shape, Spread–Variation for a period of time: Data Distributions (Graphical Analysis)– What is the shape of the distribution–symmetrical, lopsided, twin peaks, long-tailed? (determination of
normality)– What is the central tendency (“center” or “average”) of the distribution?– What is the variation (“spread”) of the distribution– Wide or narrow?
Steps 4.2: Calculate Baseline Sigma
What IS Process Capability?
A measurement scale which compares the output of a process to The performance standard
Common Metric For Comparison
Process Performance
Purchase Order 98% accuracy
Generation
Accounts Receivable 33 days average aging
Customer Service 82% rated 4 or 5 on responsiveness
Supplier Delivery 95% on-time delivery
Which process is performing best?
Data Analysis Roundup
e.g Cycle Time, Length, Weight…
Discrete DataDiscrete Data Continuous Data
Continuous Data
Defects per Opportunity
Defects per Million Opportunities
Six Sigma Product Report
Six Sigma Report:
Zlong term
Zshort term = Zbench =
reported yield
Zshift
e.g Light On
Process Capability Tools and Terminology
e.g Light off
Process Capability Continuous Data
– Verify we have a normal distribution
– Calculate ZLSL and/or ZUSL
– Determine probability of a defect
– Determine ZBench
Calculating Z
You can calculate a Z-value for any given value of x. Z is the number of standard deviations which will fit between the mean and the value of x.
z
X
Z
Calculating Capability
43210-1-2-3-4
8.98.88.78.68.58.48.38.28.1
Standard Deviations
Units of Measure
X = 8.5
s = 0.1
USLUSL Probability of a defect greater than USL
Probability of a defect greater than USLZUSL
ZUSL = USL - X = 8.7 - 8.5 = 0.2 = 2
s 0.1 0.1
LSLLSLProbability of a defect less than LSL
Probability of a defect less than LSL
ZLSL
ZLSL = X - LSL = 8.5 - 8.2 = 0.3 = 3
s 0.1 0.1
xx
Long-Term vs. Short-Term Data
Time
Y(Continuous)
Short-Term Data
Long-Term Data
Reporting Sigma Values
Short-Term Sigma = Long-Term Sigma + Sigma Shift – If “Shift” is unknown, then assume 1.5– Assume that sigma calculated from project data is long-term sigma– A rational sub grouping sampling scheme for data collection (in the Measurement
Phase) must have been used
Principles Of Rational Subgrouping
1. Never knowingly subgroup unlike things together
2. Minimize variation within each subgroup group homogeneous units, within a logic, within a reason
3. Maximize variation between sub groups the Xbar shows differences between subgroups that are bigger than that shown within subgroups
4. Treat the chart in accordance with the use of the data subgroup frequency should reflect the process use individuals with limited data use subgroups when logical
Generalizing The Correction
USLLSLLSL ± 6
.0005 ppm .0005 ppm
USLUSL
ProcessCapability
Six Sigma Centered
3.4 ppm
LSL USL4.5
TT
Six Sigma Shifted 1.5σ
TT
The Universal Equation For Z
Z =
USLLSL
T (Target)
(Mean)
st (short-term)
lt (long-term) st
lt
SL =
Z =
SL -
. . . so what are the possibilities?
and how do we choose the right one?
Z-Bench
Long-Term
Short-Term
LSL T USL_x
P(d)LSLP(d)USL
Zlt =
SL -
lt
Zst =
SL - T
st
ZLSL=
T - LSL
st
ZUSL =
USL- T
st
P(d)USL = from Z table
P(d)LSL = from Z table
P(d)Total = P(d)USL + P(d)LSL
ZB-st = from Z table
ZLSL=
-
lt
ZUSL =
USL-
lt
P(d)USL = from Z table
P(d)LSL = from Z table
P(d)Total = P(d)USL + P(d)LSL
ZB-lt = from Z table
Z-Bench-Long-Term Z-Bench-Short-Term
Z-Long-Term Z-Short-Term
LSL
Activity–Calculating Process Capability–Continuous Data
What is the process capability for a process that has: Mean = 5 Standard Deviation = 2 Upper Spec. Limit = 9
Graphically Analyze Data–Breakout Activity (20 minutes)
We always analyze the data this way:
1. Look at Stability–Is the process Stable?
2. Look at Shape–Do I have a normal distribution?
3. Look at the Spread–What measure of dispersion should I use?
Recall from our Case Study:
Traget *(More or Less) = (Target)–(Actual)
* Spec for time = Target.
Desired Outcome: Graphical Analysis of YOUR Project Y Data
What How Timing
Shape, Normality, Central Tendency And Spread
Use the Normal Probability Plot in Minitab to analyze the shape of the project Y data
Use the Descriptive Statistics tool in Minitab to analyze the shape, normality, central tendency and spread of the project Y data
Use the Minitab Six Sigma Process Report to calculate Process Sigma
RunChart
Use the Run Chart tool in Minitab to investigate the variation in the project Y data over time.
You can check your answers using the solution sheets on the following pages
Solutions
Who
All
All
All
5 mins.
10 mins.
5 mins.
Minitab Six Sigma Process Report
4.23.63.02.41.81.20.6
LSLProcess Data
Sample N 175StDev(Within) 0.0786684StDev(Overall) 0.598501
LSL 0.5Target *USL *Sample Mean 2.31714
Potential (Within) Capability
Z.USL *Cpk 7.70Lower CL 6.81Upper CL 8.59CCpk 7.70
Z.Bench
Overall Capability
Z.Bench 3.04Lower CL 1.99Upper CL 6.39Z.LSL 3.04Z.USL
*
*Ppk 1.01Lower CL 0.90Upper CL 1.13Cpm *Lower CL
Lower CL
*
*Upper CL *Z.LSL 23.10
Observed PerformancePPM < LSL 0.00PPM > USL *PPM Total 0.00
Exp. Within PerformancePPM < LSL 0.00PPM > USL *PPM Total 0.00
Exp. Overall PerformancePPM < LSL 1198.08PPM > USL *PPM Total 1198.08
WithinOverall
Process Capability of Extra Hrs(using 95.0% confidence)
The Normal Curve And Capability
Poor Design Capability
High Probability of Defects
High Probability of Defects
LSL USL
Low Probability of Defects
Low Probabilityof Defects
Good Design Capability
LSL USL
Summary–Z-Value
– Basic statistical summaries, histograms, dotplots, boxplots, and run charts are used to visualize data and better understand a process
– The Z–Value is a non-dimensional quantity that enables us to compare different processes–it represents the process capability
– The Z–Value is the number of standard deviations that will fit between the mean and the respective specification limit of a normal distribution
– The Z–Value corresponds to yield, or the area under the curve inside the specification limits
Definitions
Unit (U)– The number of parts, sub-assemblies, assemblies, or systems inspected or tested
– Squares: 4 units
Opportunity (OP)– A characteristic you inspect or test
– Circles: 5 opportunities per unit
Defect (D)– Anything that results in customer dissatisfaction. Anything that results in a non-conformance.
– Black circles: 9 defects
Formulas
Defects per Unit
DPU = D/U
9/4 = 2.25
Total Opportunities
TOP = U*OP , 4*5 = 20
Defects per Opportunity (Probability of a Defect)
DPO = D/TOP , 9/20 = .45
Defects per Million Opportunities
DPMO = DPO*1,000,000.45*1,000,000 = 450,000
Converting DPMO To Z
ZST = Sigma Capability
Long term Actual ReportedDPMO Sigma (long term) Sigma (short term)
500,000 0 1.5460,172 0.1 1.6420,740 0.2 1.7382,089 0.3 1.8344,578 0.4 1.9308,538 0.5 2274,253 0.6 2.1241,964 0.7 2.2211,855 0.8 2.3184,060 0.9 2.4158,655 1 2.5135,666 1.1 2.6115,070 1.2 2.796,801 1.3 2.880,757 1.4 2.966,807 1.5 354,799 1.6 3.144,565 1.7 3.235,930 1.8 3.328,716 1.9 3.422,750 2 3.517,864 2.1 3.613,903 2.2 3.710,724 2.3 3.88,198 2.4 3.96,210 2.5 44,661 2.6 4.13,467 2.7 4.22,555 2.8 4.31,866 2.9 4.41,350 3 4.5
968 3.1 4.6687 3.2 4.7483 3.3 4.8337 3.4 4.9233 3.5 5159 3.6 5.1108 3.7 5.272 3.8 5.348 3.9 5.432 4 5.521 4.1 5.613 4.2 5.79 4.3 5.85 4.4 5.9
3.4 4.5 6
2 308,538 3 66,807 4 6,210 5 233 6 3.4
ZZ DPMODPMO
First Pass vs. Final Yield
Example
Customer CTQs Invoice mailed on date specified Invoice is error free
– Correct address
– Correct amount
Prepare Invoice
500 Preliminary Invoices
Review Invoice
Fix Errors
Mail Invoice
446 Accurate Invoices
470 Invoices Mailed On-Time
30 Invoices Mailed Late
Errors Detected28 – Wrong amount14 – Wrong address12 – Improper accounting code
Summary–Discrete Data Process Capability
– Define Defects, Units and Opportunities with your team. Be sure the definitions make sense and are consistent with similar processes and customer definitions.
– Defects will be stated as Defects Per Million Opportunities. Discrete data is generally considered long-term data.– For discrete data, Minitab Six Sigma Product Report is used to calculate capability from defects and opportunities– Determine DPMO (which is long-term), then determine the corresponding Z–value (ST capability)
D-M-A-I-C…Overview
Step 1: Identify VoC & CTQs
Step 2: Define the Project
Step 3: Define Process map
Step 4: Building Team & Commitment
Step 5: Assess Risk
Step 1: Identify and prioritize CTQ Metrics
Step 2: Define Performance Standards
Step 3: Measurement System Analysis & Data Collection Plan
Step 4: Establish Current Process Capability
Step 5: Quantify the Opportunity
Step 1: Brainstorm potential solutions
Step 2: Screen solutions against criteria
Step 3: Develop Implementation Plan
Step 1: Develop Control Plan
Step 2: Develop Process Management Flowchart
Step 3: Assess Potential Problems
Step 4: Implement Process Control System
Step 1: Identify Root Cause / Sources of Variation
Step 2: Validate Root Causes
Step 3: Define Performance Objectives
Step Description
Define
Measure
Analyze
Improve
Control
Identification of Variation Sources
Analyze – Identify Variation Sources
What does it mean to Identify Variation Sources?
In step you develop a list of statistically significant X’s, chosen based on analysis of historical data. This list is then prioritized to identify those X’s that have the most impact on the project Y. The question in this step is “What are the variables that are preventing us from reaching our goal?” You will identify all possible X’s before selecting the Critical (or Vital Few) X’s in the next step.
Why is it important to Identify Variation Sources?
The output of a process (Y) is a function of the input sources of variation (X’s). In other words, you can change the output of a process (Y) only by changing the input & process variables (X’s). Therefore, in order to improve products and processes, you must shift your focus from monitoring the outputs of a process (Y’s) to optimizing the inputs to the process and correcting the root causes of defects (X’s). You should use data and process analysis to identify potential X’s, and not make any assumptions.
What are the project tasks for completing Analyze 6?
1 Identify possible causes of variation2 Narrow list of potential causes
Identify The Vital Few
Transfer Function
=
Project Y
Relationship that explains Y in terms of
X
Process variables
YY ff (X)(X)
Understanding the ƒ gives Insight into the Vital Few X’s
165
Terminology
Project YDependent
Independent X(5M’s and 1P)
Independent Variables–X’s Also called factors Factors or variables we select in advance The causes
Dependent Variable–Y Also called responses The quantity (Y) that we measure to determine
the impact of the X’s The effect
Project Y
MMM
M MP
(x) (x) (x)
(x) (x) (x)
166
Bridging The Real World
Practical SolutionPractical Solution
Statistical SolutionStatistical Solution
Practical ProblemPractical Problem
Statistical ProblemStatistical Problem
ProblemSolving
Flow State current process sigma.
Identify distribution’s characteristic causing current process sigma: shape,
center and/or spread.
Find X’s that lead to better process sigma: Identify the levels of X’s
Identify process change that incorporates statistical solution
© 1994 Dr. Mikel J. Harry V3.0
167
The Nature Of Statistical Problems
Problem with Spread
DesiredCurrent
Situation
LSLLSL USLUSLTT
Accurate but not PreciseAccurate but not Precise
Problem with Centering
Desired
LSLLSL USLUSLTT
Precise but not AccuratePrecise but not Accurate
CurrentSituationOff Target
168
Using Statistics To Solve Problems
Y = ƒ (X1, …, Xn)
Goal: To find the relationship
P(x)
x
Data-Driven AnalysisData-Driven Analysis
Identify The Vital Few
Process Measures(X’s)
Process
InputMeasure
s(X’s)
Outputs (Y’s)
X X X X
Analyze 1.1: Identify Possible Causes of Variation
• Identify Sources of Variation
• Brainstorm for Possible sources of Variation – Fishbone Diagram, 5-Why
• Prioritize all Possible Xs – Control/Impact Matrix
• Validate Prioritized Xs
• Validation of Process as X
• Type of Work – Waste
• Nature of Work – VA/NVA/VE
• Flow of Work – Sub Process Map
• Data Analysis
• Hypothesis Testing
• List of Validated Xs
Content Flow
Methods To Identify Possible Sources Of Variation
Methods To Identify Vital X’s
Graphical Analysis
Process Map Analysis
Machines Methods Materials
Measurement Mother Nature People
Problem
Statement
How to Start…Machines Methods Materials
Measurement Mother Nature People
Problem
Statement
Graphical Analysis
Machines Methods Materials
Measurement Mother Nature People
Problem
Statement
Start Here
Or Here
And
Again Here
1
How to Start…
Machines Methods Materials
Measurement Mother Nature People
Problem
Statement
Start Here
2
2.1
In Our Control
Out Of Our
Control
C
O
N
T
R
O
L
IMPACTHigh Medium Low
Always Verify with Data/Process Analysis
How to Start…
Machines Methods Materials
Measurement Mother Nature People
Problem
Statement
Start Here
Process Map Analysis
2
Drill Down for Analysis of -
• Measurement process
• Processing/Method
• Processes around above factors
2.1
Review: Graphical Analysis
Looking For Patterns In Data
Continuous Y Discrete Y
Boxplot Pareto Chart
Scatterplot
Histogram
Process Map Analysis
Types Of Analysis
Type of Work – waste Identification
Nature of Work
Flow of Work
Nature Of Work–Value Analysis
Value-Added Work Nonvalue-Added Work
Value-Enabling Work
Steps That Are Considered Non-Essential To Produce And Deliver The Product Or Service To Meet The Customer’s Needs And Requirements. The Customer Is Not WillingTo Pay For Them.
Steps That Are Considered Non-Essential To Produce And Deliver The Product Or Service To Meet The Customer’s Needs And Requirements. The Customer Is Not WillingTo Pay For Them.
Steps That Are Essential Because They Physically Change The Product/Service, The Customer Is Willing To Pay For Them, And They Are Done Right The First Time.
Steps That Are Essential Because They Physically Change The Product/Service, The Customer Is Willing To Pay For Them, And They Are Done Right The First Time.
Steps That Are Not Essential To The Customer, But That Allow The Value-Adding Tasks To Be Done Better/Faster.
Steps That Are Not Essential To The Customer, But That Allow The Value-Adding Tasks To Be Done Better/Faster.
Types Of Non value–Added Work
Internal FailureInternal Failure DelayDelay
External FailureExternal Failure Preparation/Set-UpPreparation/Set-Up
Control/InspectionControl/Inspection MoveMove
What Does The Customer Value?
Flow Of Work
Cycle TimeCycle Time
Process TimeProcess Time
Delay TimeDelay Time+
Flow Of Work–Process Disconnects
Gaps
Redundancies
Implicit or unclear requirements
Inefficient hand-offs
Conflicting objectives
Common problem areas
Flow Of Work–”Be The Unit”
Unclear requirements
1. Receive application in mail and open
envelope
2. Place application in
mail slot
3. Move application to
Entry Dept.
4. Place application in
in-box
5. Retrieve application and
review for completeness
Is application complete?
7. Enter application
to computer system
6. Call to obtain necessary information
8. Score application
9. Queue application for credit review
10. Review for completeness
and make decision
Are we extending
loan?
19. Generate turndown letter
12. Generate loan packet
13. Place in out-box
14. Move to mailroom
15. Wait for postage
16. Post package or
letter
17. Place in outbound mail
basket
18. Postman picks up
outbound mail
No
Yes
Yes
No
Unclear requirements
Inefficient hand-off
Redundancy
Inefficient hand-off
11. Make loandecision
Linking Value Analysis With Process FlowSummarized Analysis
Process Step
Est. Avg. Time (Mins)
Value-Added
Nonvalue-Added
Internal Failure
External Failure
Control/Inspection
Delay
Prep/Set-Up
Move
Value-Enabling
Total
1 2 3 5 6 7 8 9 10 144 1211 13 15 16 17 18
1 1803
7120 12015 51051201 1202120159015
Total%
Total
3.1%
957
72.1%690
.8%8
100%
48 5.0%
30
100%
180 18.8%
1 .1%
19
9578
% Steps
Review: Cause & Effect DiagramsA Visual Tool Used By An Improvement Team To Brainstorm And Logically Organize Possible Causes
For A Specific Problem Or Effect
Machines Methods Materials
Measurement Mother Nature People
Potential High-Level Causes Problem
Statement
Cause & Effect Diagrams–The Five Why’s
The “Five Why’s” Drill Deep Into The Process To Identify Potential Root Cause(s)
Ask “why” five times to identify deeper causes
Use process data to answer each “why” question
Prioritization Of X’s–Control/Impact Matrix
In Our Control
Out Of Our
Control
C
O
N
T
R
O
L
IMPACTHigh Medium Low
Always Verify with Data
Prioritization Of X’s–Control/Impact Matrix (continued)
Too manydefects
Complicatedform
Too muchreview
Duplicationof effort
Too long forcustomernumber
Complexity
Evaluationof riskworthiness
Too long toget creditreport
Not enoughstaff
Not welltrained
In Our Control
Out Of Our Control
C
O
N
T
R
O
L
IMPACT High Medium Low
Example
MethodsMachines
People
MaterialsWhy Is There Difference In The Variation In Cycle
Time Between Small And Medium Loans?
Why Is There Difference In The Variation In Cycle
Time Between Small And Medium Loans?
MotherNature
Measure-ments
Prioritization Of X’s–Control/impact Matrix
In Our Control
Out Of Our
Control
C
O
N
T
R
O
L
IMPACT
High Medium Low
Analyze 1.2 Narrow list of Potential Causes
Hypothesis Testing–Introduction
– Refers to the use of statistical analysis to determine if observed differences between two or more data samples are due to random chance or to be true differences in the samples
– Increase your confidence that probable X’s are statistically significant– Used when you need to be confident that a statistical difference exists
Hypothesis Testing For Equal MeansThe histograms below show the height of inhabitants of countries A and B.
Both samples are of size 100, the scale is the same, and the unit of measurement is inches.
Question: Is the population of country B, on average, taller than that of country A?
Country A
Country B
[inch]60.0 62.0 64.066.0 68.0 70.0 72.0 74.0 76.078.0 80.0
Concepts Of Hypothesis Testing
1. All processes have variation.
2. Samples from one given process may vary.
3. How can we differentiate between sample–based “chance” variation and a true process difference?
Kinds Of Differences
Continuous data:
Differences in averages
Differences in variation
Differences in distribution “shape” of values
Discrete data:
Differences in proportions
Hypothesis TestingGuilty vs. Innocent Example
The American justice system can be used to illustrate theconcept of hypothesis testing.
In America, we assume innocence until proven guilty.This corresponds to the null hypothesis.
It requires strong evidence “beyond a reasonable doubt”to convict the defendant. This corresponds to rejecting the null hypothesis and accepting the alternate hypothesis.
Ho: person is innocentHa: person is guilty
Activity–Hypothesis Statements (10 minutes)
Write the null and alternate hypothesis testing statements for each scenario below:
Scenario 1: You have collected data on the number of defects seen in products from supplier A and supplier B. You wish to test whether or not there is a difference in defects from supplier A and B.
Null hypothesis statement :
Alternate hypothesis statement:
Scenario 2: You suspect that there is a difference in cycle time to process purchase orders in site 1 of your company compared to site 2. You are going to perform a hypothesis test to verify your hypothesis.
Null hypothesis statement :
Alternate hypothesis statement:
Scenario 3: You purchase resins to be used in your company's manufacturing processes. You suspect that suppliers who use higher temperatures to cure the resin are able to cure the resins faster.
Null hypothesis statement :
Alternate hypothesis statement:
Scenario 4: You have implemented process improvements to reduce the cycle time to process purchase orders in your company. You have collected cycle time before the process improvements and after the process improvement was implemented. You are going to perform a hypothesis test to verify that the process improvements have resulted in a reduction in cycle time.
Null hypothesis statement :
Alternate hypothesis statement:
Hypothesis Testing
Guilty vs. Innocent Example
The only four possible outcomes:
1. An innocent person is set free. Correct decision
2. An innocent person is jailed. Type I error– The probability of this type of error occurring we represent as
3. A guilty person is set free Type II error– The probability of this type of error occurring we represent as
4. A guilty person is jailed. Correct decision
α
β
Hypothesis Testing–Another View
TruthTruth
Ho Ha
VerdictVerdict
Ho
Ha
Innocent,JailedType I
α
Guilty,Set FreeType II
β
Innocent,Set Free
Guilty,Jailed
Innocent Guilty
Set Free
Jailed
Ho: Person is innocent.Ha: Person is guilty.
Hypothesis TestingP-value
The probability of making a Type I error (concluding that there is a statistical difference between samples when there is no difference).This value ranges from 0.0–1.0
Typically set Type I error probability of = 0.05–P-value less than 0.05 means we reject the null hypothesis and accept the alternate hypothesis
p < : Reject Ho
p : Accept Ho
Statistical Tests In Minitab
Some basic statistical tests are shown below with the command for running each test in Minitab.
Variance among two or more populations is different.
Homogeneity of Variance
Stat > ANOVA > Homogeneity of Variance
Output (Y) changes as the input (X) changes.
LinearRegression
Stat > Regression >Fitted Line Plot
Output counts from two two or more subgroups differ.
Chi-Square Testof Independence
Stat > Tables > Cross Tabulation OR
Chi-Square Test
BoxPlots
ScatterPlots
C AB D E
Fre
qu
ency
Category
Pareto
M N O
What The Tool Tests Statistical Test Graphical TestMean of population data is different from an established target.
1-Sample t-testStat > Basic Statistics
> 1-Sample t
Mean of population 1 is different from mean of population 2.
2-Sample t-testStat > Basic Statistics
> 2-Sample t
The means of two or more populations is different.
1-Way ANOVAStat > ANOVA > One-Way
Histogram
Histogram
Histogram
Normality TestStat > Basic
Statistics
Data is normally distributed
Select A Statistical TestHypothesis tests to find relationships between project Y and potential X’s
Simple Linear Regression
2 Sample t-Test (Compare Means of two
samples)
ANOVA (Compare means of multiple samples)
Homgeneity of Variance (Compare variances)
ContinuousContinuous DiscreteDiscrete
Discrete
Continuous
X
Chi-Square Test
Y
Hypothesis Test Summary
Variance Tests
Homogeneity of Variance Levene’s–Compares two or more sample variances.
Medians Tests
Mood’s Median Test–Another test for two or more medians. More robust to outliers in data.
Correlation–Tests linear relationship between two variables.
Variance Tests
F–test-–Compares two sample variances.
Homogeneity of Variance Bartlett’s–Compares two or more sample variances
Means Tests
t–Test 1–sample–Tests if sample mean is equal to a known mean or target.
t–Test 2–sample–Tests if two sample means are equal.
ANOVA One Way–Tests if two or more sample means are equal.
ANOVA Two Way–Tests if means from samples classified by two categories are equal.
Correlation–Tests linear relationship between two variables.
Regression–Defines the linear relationship between a dependent and independent variable. (Here, “Normality” applies to the residuals of the regression.)
Non-normal DataNormal Data
Choosing The Correct Hypothesis Test
Mood’s MedianHOV
CHI SQUARE
ANOVAHOV
Is the data normal?
Are Y’sContinuous?
Comparing Only 2
Groups?
Can I Match X’s With X’s?
Are We Comparing To A Standard?
Paired t 1 Sample t
NO
NO
NO
NO NO
YES YES
YES
YES
YES
2 Sample tHOV
Note: In order to use this chart, we are assuming our X’s are discrete. Otherwise, use Regression. (1x = Simple Linear Regression While Multiple X’s Would use Multiple Linear Regression).
Hypothesis Testing Procedure
Team preparation
1. Write the null hypothesisHo: There is no difference between Population A and B
2. Write the alternate hypothesis
3. Decide on the alpha level
4. Chose hypothesis test
5. Gather evidence and test/conduct analysis
6. Decide to Reject H0, or not reject H0, and draw conclusion
α =.05 (typical for DMAIC projects)
Choose the correct test, given the type of X and Y data.
Collect data, run analysis, get p-value
If p 0.05 conclude, no difference between populationsIf p < 0.05 conclude, the populations are different
HA: There is a difference between Samples A and B
pop2pop1 μμ
pop2pop1 μμ
1-Sample Hypothesis
1. Ho : = constant = T
Ha : constant = T
HHoo HHaa
TT
2. Ho : = constant = T
Ha : 2 constant = T
Review: Scatter Plots
y
x
y
x
r = 0r = 0
y
x
r = –1.0
x
y r = +1.0
y
x
y
x
r = –.7r = +.7
R-value
Simple Linear Regression– We have shown/talked about positive and negative correlation of two data sets– Regression analysis is a statistical technique used to build the Y = ƒ(x) relationship between two or
more variables. The model is often used for prediction.
– Regression is a hypothesis test. Ha: The “X” is a significant predictor of the response.
– It may be used to analyze relationships between the “X’s”, or between “Y” and “X”– Regression is a powerful tool, but can never replace process knowledge about trends
Simple Linear Regression
Ha: The model is a significant predictor of the response.
b0 = Predicted value of Y when X1 = 0
b1 = Slope of line change in Y per unit
change in X1
Minitab File: GB case study.mtw
Null Hypothesis: There is no correlation between our continuous Y metric (time) and a continuous X metric (distance)
Minitab Command: Stat > Regression > Fitted Line Plot
Y
X
Y = b0 + b1X1
Chi-Square Test
ContinuousContinuous DiscreteDiscrete
Discrete
Continuous
X
Chi-Square Test
Y
Chi-Square Tests
The Chi-Square TestsUsed for:
1 - Goodness-of-Fit Test: To test if an observed set of data fits a model (an expected set of data)
2 - Test of Independence: To test hypothesis of several proportions (contingency table)
It’s for discrete data, any number of categoriesFor all cases, Ho: no difference in data
Ha: difference exists
2